Visual Quantum Mechanics

This page is reserved for statements of readers. I would be glad to receive more comments. If you want to comment on the book, just send an e-mail to the author. I will publish qualified opinions and constructive critisism on this page, but I reserve the right to cite only parts from longer statements.

A friend sent me the following line:
"How I like a drink, alcoholic of course, after the heavy lectures involving quantum mechanics..."

Note that the number of letters in each word gives Pi =3,14159265358979...

Michael A. Morrison <morrison "at"> (2003-01-01) wrote:
The book is a delight and a revelation. I have enormously enjoyed studying the text, especially the chapters on the mathematical fundamentals of quantum theory and on one-dimensional scattering theory. And the visualizations are a terrific learning tool. The next time I teach quantum mechanics I intend to adopt the book if I can so as to make the fine text and visualization machinery available to my students.

During several years recently when I taught this course I used Mathematica in various ways and so scoured the literature for books on using it in teaching. All I found were very unsatisfactory: either books about how to use Mathematica that gave only incidental attention to physics or books that didn't teach physics or Mathematica but rather seemed to show off their authors' abilities to solve complicated theoretical physics problems on the computer. Your book has the ideal combination: focus strongly on the physics but accompanying Mathematica packages so users can adapt them as desired.

I have the greatest respect for your accomplishment with Visual Quantum
Mechanics and eagerly await its sequel.

Book Review 1:
Read a book-review by Evans M. Harrel II in Siam Review (SIREV Vol. 43 Number 2).

Book Review 2:
Here are a few quotations from a long and detailed review by Brian DeFacio. It appeared in Mathematical Reviews (review number 2001k:81002) and is accessible to subscribers via MathSciNet (download pdf):
This is a marvelous book on quantum mechanics. It won the European Academic Software Award in November, 2000 with a special mention for outstanding innovation in its field. Normally, color graphics conceal more information than they reveal. The use of color in the accompanying CD-ROM is very effective. ...
The numerous examples on the accompanying CD-ROM convey much information and in addition are beautiful. I wish this book and CD-ROM had been available when I was studying complex analysis or quantum mechanics long ago. The CD-ROM examples and short films are an essential part of this book. That said, this book lacks the breadth to stand alone as a primary text for upper level undergraduate or lower level graduate quantum mechanics classes. One of its great strengths is the depth at which it examines fundamental quantum mechanics. I plan to use it as a second required text the next time I teach quantum mechanics. The book would also be useful for self-study, and mathematicians will especially enjoy it. The author is a first-rate mathematical physicist who discusses the Hilbert space structure of simple quantum states of a system, their self-adjoint observables, their time evolution and the structure of quantum measurement with clarity and accuracy. ...
In summary, this is an excellent book--CD-ROM package, which I'll use next time I teach quantum mechanics. In the meantime, this reviewer's copy will be passed around my department for others to consider adding to their teaching. Readers of the Mathematical Reviews will also find Thaller's book both interesting and useful for the opportunity to understand the basic ideas of quantum mechanics. The author's second book is eagerly anticipated.

More Reviews:
A preliminary version of the text has been reviewed by anonymous expert referees. Here are some of their more general comments. (The reviewers also made some very specific suggestions to improve the text, which I tried to take into account when I prepared the final version of the manuscript).

Reviewer #1:
Another Quantum Mechanics book? This may be the reaction of many who would see this book at the store, and a glance at the bibliography of QM books in the Appendix ought to reinforce this point of view. I myself changed my mind right after seeing the material on the CD, and after reading the book in full, I am inclined to say that I would probably buy this book for myself even without the CD.
This is not an introductory book, and it is hard for me to judge how this material would fly with someone not yet exposed to the basic ideas and formalism of quantum mechanics, as the time when this occurred to me is long in the past. I *use* quantum mechanics, and as such it is a useful book. Some of the more advanced discussions about mathematical aspects of the formalism are here brought together with a more mundane exposition of the basic principles, something that one would have wished to see in other books. I know that I'm reviewing a useful book when I hesitate to send back the original of the annotated copy. What am I gonna do without it until the published version arrives?
I would buy it, I will recommend it, and I congratulate the author.

Reviewer #2:
The author has obviously worked very hard to create an interesting volume, skillfully written and scientifically virtually impeccable. The visuals are spectacular, informative and entertaining. The approach is very mathematical, for a text that I assume is intended for a first graduate course in quantum mechanics. It will clearly be a question of the taste of the individual instructor to decide on whether this strongly mathematical approach is suitable. My personal inclination would be for a more physically oriented one, as for example that taken by the new Merzbacher book, but this may reflect my own background as an experimental physicist.

More Comments:

Robert F. Scheyder <scheyder "at"> (2000-06-05) wrote:
I have been playing with your software, "quantumkernel". I find that it is really helpful for visualizing quamtum mechanics, as you designed it to be. Your program let's me visualize quantum mechanics, which is good because just looking at the bare equations is not helpful. It would be time-consuming to use Mathematica from first principles, but your software saves the effort. I'm taking a course in partial differential equations presently, and using your software let's me present excellent results that are useful in this PDE course.

Robert F. Scheyder <scheyder "at"> (2000-07-26) wrote:
I purchased a copy of your "Visual QM, vol. 1". All I can say is WOW! When will vol. 2 be available? The movies are really good and help to illustrate the abstract QM concepts. Also, the QM software that you distributed via MathSource and that which came on the CD work exactly alike. The reason I say this is because I recently purchased a PDE book that used interactive Mathematica notebooks, and it did not work under Mathematica v.4.0!

Victor Benham, Ph.D. <cw400 "at"> (2000-12-31) wrote:
I'd like to thank and congratulate you for writing such a useful and expressive book. As I am sure you will agree a lot of undergraduate and graduate students find the fascinating subject of Quantum Mechanics mysterious and in so many ways incomprehensible. I believe your book provides a strong basis to put an end to this school of thought.

Paul Scholz <pscholz "at"> (2001-03-08) wrote:
I just got your book and CD-Rom. Wow! Finally, a reason to study math beyond calculus. I've been casually interested in quantum mechanics but I am not that gifted in mathematics. But, with your book and dynamic illustrations, I can understand what is going on and figure out the mathematics for myself, which is terrific.
I'm looking forward to many months of going through your book to finally
understand the math behind the ideas. Thanks!

John Cousins <ja-cousins "at"> (2001-03-08) wrote:
       The CD & book called "Visual Quantum Mechanics" seems brilliant, but as I wasn't able to fully understand most of the animated sections even with your related textual explanation, I can't help but feel your definition of a beginner is someone with a bit more knowledge than I.
       I am an electronics engineer with a great desire to understand these concepts but sadly many years from having indulged into serious maths. I have read and understood a number of books dealing with quantum mechanics all having limited mathematical content, but alas I feel that unless your book takes one through the maths which I am prepared to face if necessary I don't think this is probably for me. What is your oppinion?
       There must be someone out there who is prepared to tackle the needs of charactars like me who want to know this stuff but need the helping hand over the hurdles!

Anonymous reader at
This is a great combination: Many diagrams, animations and so on on the CD-ROM, which are not just to look at, but you can modify parameters and interact with some of them, which is great for understanding and the book with the theoretical background to everything you can see an the CD-ROM and more. You should be fimilar with higher mathematics (complex numbers and stuff) if you really want to understand the complicated-looking mathematical background, but the CD-ROM shows that the core of the whole Quantum-Mechanics-Thing seems to be very natural (what a surprise). This book is an excellent approach to this topic - take a glance. ... and for those, who are not interested in QM-theory: the animations are very colorful and fine to look at

At 6:27, 22.03.2004, roger.cattermole "at" wrote:
I love your selection of strange Mathematical images, but its a shame you dont
give a brief description for each stating what kind of mathematical function
is being represented..
Thx for the interesting site though!

(Author's reply: You can see the definition of all images by downloading and inspecting the Mathematica source code.)

At 10:33, 10.05.2004, Ben van Linden van den Heuvell wrote:
For a long time I have tried to make pictures of volume data, in particular of 3D wavefunctions. I also followed the attempts of others. Neither my results nor others were very convincing. I was therefore very enthusiastic when I saw your QuantumGL. The manual of the program suggests that the source of this program is available. If this is the case indeed, then I would like to ask you if you are willing to send me the program or the place where I can find it.
I'm looking very much forward to your new book.
For many years I already enjoy the old one. In particular the possibility to calculate the time evolution of the Schrödinger equation was and still is very useful. Even now it is possible to do the same calculation (also in 2D and 3D) in Mathematica version 5, your code is not only faster, but also much less demanding in terms of memory.

(Author's reply: You can download QuantumGL and the source code here.)

Readers from Germany:

Jan Staiger <jan.staiger "at"> (26 Jul 2002):
Ich möchte ihnen einfach zu ihrer Website über die VQM gratulieren!

Ich studiere Medienwissenschaft und schreibe gerade an meiner Diplomarbeit über journalistische "Kriegskonstruktionen". [...]

Eigentlich möchte ich ihnen aber vor allem eines sagen: Der Anblick ihrer Visualisierungen, insbesondere der Bilder und Animationen zum Wasserstoff-Atom haben mir soeben ob ihrer Schönheit (bzw. ob der "Schönheit" der zugrundeliegenden "Muster") fast die Tränen in die Augen getrieben.

Reinhard Dörner <doerner "at"> (10 Nov 2002):
Glückwunsch zu und herzlichen Dank für Ihr Projekt Visual QM -
Besser kann man die QM didaktisch nicht aufbereiten um jenseits der Mathematik ein "Gefühl" fuer die QM zu bekommen. Ich werde Ihre Movies und Bilder in meiner Vorlesung einsetzen.